It is known to treat bulk material with gas by conveying it continuously in a layer over a grate, with gas flowing through it in the process. What are known as reciprocating grates, which comprise overlapping rows of, alternately, stationary grate plates and grate plates which move forward and back in the conveying direction (DE-A-37 34 043, DE-A-196 49 921), are predominantly used for the cooling of combustion material, for example cement clinker. Cooling air which effects the cooling and is discharged above the layer of material in order for the heat to be recovered is blown into the bed of material through the grate plates. Another known design of grate makes use of a stationary air-permeable bearing floor over which the layer of material is moved by means of scrapers which move continuously in the conveying direction or reciprocating members (EP-A-718 578, WO 00/31483). Yet another type of cooler uses a migrating grate which moves continuously in an endless loop (DE-A 1 953 415). In all cases, it is endeavored to recover the heat transferred from the material being cooled to the cooling gas as completely as possible. Irrespective of the type of cooler, the recovery of heat has reached a relatively advanced state.